Question

Let x be a normal random variable with mean equal to 40 and standard deviation equal to 5

a) P(x>55)=?

b) P(x<49)=?

Answer 1

Solution :

Given that ,

mean = = 40

standard deviation = = 5

(a)

P(x > 55) = 1 - P(x < 55)

= 1 - P((x - ) / < (55 - 40) / 5)

= 1 - P(z < 3)

= 1 - 0.9987   

= 0.0013

P(x > 55) = 0.0013

Probability = 0.0013

(b)

P(x < 49) = P((x - ) / < (49 - 40) / 5)

= P(z < 1.8)

Using standard normal table,

P(x < 49) = 0.941

Probability = 0.9641